The Magyars already had a complex political society when they arrived in the Carpathian Basin, with (based on our major Byzantine sources, including Emperor Constantine Porphyrogenitos and Arabic sources like Ibn Rustam) three ranked roles of ‘ruler’ known as the kende (possibly once the most powerful role, but largely just a nominal king by this point), the gyula (at the time of the invasion of the Carpathian Basin, Árpád, de facto chief conqueror of the region and founder of the later royal dynasty), and the horka (who possibly had some sort of judicial role, eventually absorbed into that of the gyula).

Under them were their family members and various other military commanders. Further, there were other apparent warrior subgroups like the Szekelys who developed their own structure, though it is unclear exactly how and when these (or even Szekely identity) formed. This was certainly enough social stratification for authority and land to be divided accordingly, with Árpád’s dynasty soon falling into deadly fraternal conflict as disagreements over the division of territory compounded. With Christianisation in the decades after the Battle of Lechfield and the coronation of Stephen I a generation later, the Holy Roman Empire’s feudal model was adopted as an implicit part of the new legal canon, but they were already not lacking for nobles to occupy that role. Naturally, the previous inhabitants - at this point largely Slavic, from their own migrations a few centuries earlier - mostly continued to be peasants, or were enslaved and largely 'Magyarised' or (according to Ibn Rusta) sold to the Byzantines. (Being the largest group of nearby 'pagans' in the 9th century, Slavs were a major source of slaves in the Byzantine Empire, with Varangian, Magyar and Radhanite traders defeating and providing many of them... and in fact it is via this route that the word 'slave' made its way to English.)

Remember that at this point in history, slavery still continued alongside serfdom, and the two had a complex relationship until serfdom came to dominate completely by 1000 AD, around the time Hungary Christianised. Certainly slavery was a common part of Steppe societies, and it is very probable that slaves were brought in with the Magyars from wars with Slavs and others en route, and these too would have eventually become serfs as part of this trend.

Later, in the reign of Andrew II (early 13th century), royal lands were redistributed to his favoured subjects, and the feudal system was further entrenched.

A similar story holds true for other Steppe peoples and similar organised ‘tribal nomads’. Very few such militaristic societies, sedentary or nomadic, are completely egalitarian to begin with. (I stuck to the Magyars/Hungarians here, but may expand this comment to include more examples when I have time.)